The sum of the squares of two consecutive positive odd integers is equal to one hundred thirty. Find the two integers.

unknown values: 2*x-1,2*x+1

equation: (2*x-1)^2 + (2*x+1)^2 = 130

answer: 7;9

The sum of the positive odd integers less than 50 is subtracted from the sum of the positive even integers less than or equal to 50. What is the resulting difference?

unknown values: x

equation: 2*n = 50

equation: x = (2+50)*n/2 - (1 + (50-1))*n/2

answer: 25

Twice the square of an odd integer is 1 more than the square of the next consecutive odd integer. What is the greater integer?

unknown values: 2*k+1

equation: 2*(2*k-1)^2=(2*k+1)^2+1

answer: 7 or 1

find four consecutive odd integers so that the sum of the smallest integer and the largest integer is the same as the sum of all four integers

unknown values: 2*k-3,2*k-1,2*k+1,2*k+3

equation: (2*k-3)+(2*k+3)=(2*k-3)+(2*k-1)+(2*k+1)+(2*k+3)

answer: -3; -1; 1; 3

Find three consecutive integers such that the sum of the squares of the second and third exceeds twice the square of the first by 41.

unknown values: x-1,x,x+1

equation: x^2+(x+1)^2=2*(x-1)^2+41

answer: 6; 7; 8

Find four consecutive odd integers such that the product of the second and third exceeds the square of the first by 98.

unknown values: 2*k-3,2*k-1,2*k+1,2*k+3

equation: (2*k-1)(2*k+1)=(2*k-3)^2+98

answer: 15; 17; 19; 21

when the sum of 16 and 10 times a positive number is subtracted from the square of the number, 0 results

unknown values: x

equation: 16+10*x-x^2=0

answer: 11.403

Find the integers. Five consecutive odd integers such that the sum of the first and fifth are one less than three times the fourth integer.

unknown values: 2*k-3,2*k-1,2*k+1,2*k+3,2*k+5

equation: (2*k-3)+(2*k+5)=3*(2*k+3)-1

answer: -9; -7; -5; -3; -1

the greater of two consecutive even integers is 10 more than half the greater. Find the integers

unknown values: 2*k,2*k+2

equation: (2*k+2)=(1/2)*(2*k+2)+10

answer: 18; 20

there are 3 consecutive integers. the sum of the first two integers is 16 more than the third. Find integers

unknown values: x-1,x,x+1

equation: (x-1)+x=(x+1)+16

answer: 17; 18; 19